The sequence a_n satisfies a_0 =1 and \(a_n = a_0 + a_1 + \dots + a_{n - 1}\) for n > 0. Find a_{100}.
It looks like your sequence should go like this:
1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512......and so on. Each term is obtained by 2 raised to the term number -1. Examples: 5th term =2^(5-1) =2^4 =16. 10th term =2^(10-1) =2^9 =512.
Therefore, the 100th term =2^(100 - 1) =2^99 =633,825,300,114,114,700,748,351,602,688
